Weapons WI: The British chose another rifle over the Martini-Henry

I recently did a study on the history of the weapons used by the British military and came across this video about the trials done on guns done by the British army which lead to the choice of the Martini-Henry. It states many of the problems it initaily had when first used in combat and this made me wonder what could have been different if the army had chose another rifle. The Carter and Edwards bolt action shown in the video seems like a choice which could easily be made if the accident of one of the judges thumbs being blown off by another rifle could be butterflied. For those with a knowledge of weapons could you tell me how the British campaigns of the late 1800s could have been different if the British had adapted this bolt action rifle design combined with the Henry barrel.
Here is a paper with details on the Carter and Edwards.

Would it be too much of a leap to have the British Army continue relying on the old Snyder, or was the push for modernization of arms too great?

Any ideas?